The Scottish outfit travelled to Thomond Park on Friday evening and beat last year's PRO12 semi-finalists Munster 14-13 in a nail-biting clash.
Heathcote, who joined from Bath over the summer, sent three penalties between the posts before watching anxiously as opposite number Ian Keatley missed a last-gasp kick to win it.
The result matched Edinburgh's tally of away wins in the competition from the whole of last season and their new No.10 is already looking to kick on - starting with Connacht's visit to Murrayfield on Friday.
"Hopefully a good win in the first week will drum up a bit of good support for Friday night," he told the club website.
"We said we wanted to build on this now. There are plenty of things to work on but plenty of good things as well, so we have a good week ahead of us leading into next Friday night and we'll hit the ground running again.
"The forwards worked really hard, both in attack and defence. We gave them a lot of work do to in attack and they really fronted up and did really well - and defensively from the whole team, we pride ourselves on that and I was really impressed with the whole performance.
"We had to make a lot of tackles in our own 22 and all over really, so it was a really encouraging performance."
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